Cumulant approach to the two-dimensional magneto-conductivity problem

The validity of assumptions involved in experimental evaluations of the g-factor of electrons in (100) surface inversion layers of p-silicon from Shubnikov-De Haas oscillations of the surface conductivity by the method of tilted megnetic fields is discussed on the basis of the transport theory of a two-dimensional electron-impurity system. The self-consistent Born approximation is shown to be insufficient to this task, and an alternative cumulant approach is discussed. Contrary to recent work, the cumulant approach is introduced in a simple manner, avoiding the path-integral formalism.     

Path-integral formulation of two-dimensional gauge theories with massless fermions

We study (1 + 1) dimensional gauge theories [with SU(N) and diagonal SU(N) color symmetry] using the functional integral method. We construct an effective lagrangian by performing a change in the fermionic variables, and then investigate relevant phenomena such as the intrinsic Higgs mechanism and color screening.     

二维无限深方势阱中粒子运动的路径积分解法

用路径积分的方法计算了二维无限深方势阱中粒子的传播子,并由传播函数推导出二维无限深方势阱中粒子的波函数和能量,进一步体现了路径积分与其他经典量子化方法的等价性,反映了路径积分应用于难以处理的量子力学问题的价值.     

Simple approach to the band-structure problem

An approximate first-principles method is presented for calculating the band structure of solids, especially applicable to closely-packed structures. This scheme has the advantages of being physically transparent, and computionally very fast. In its simplest form it gives energies correct to within a few per cent of the band width, and the error may be substantially reduced without much increase in complexity or computing effort.     

Density-functional approach to two-dimensional classical fluids

The density-functional (DF) method is combined with the smoothed-density approximation to calculate the fluid structure in two-dimensional (2D) hard-disc (HD) systems. Density-dependent weighting functions in the DF method proposed by Tarazona for three-dimensional fluids have been applied to 2D systems for the calculation of the radial distribution function of HD fluids and the determination of the static structure of 2D HD fluids around the central hard triatomic molecule. The results compare reasonably well with Monte Carlo data. The radial distribution of a 2D Lennard-Jones fluid has also been calculated and shown to be in satisfactory agreement with Monte Carlo data except for the high-density fluid.     

A fractional approach to the Fermi-Pasta-Ulam problem

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.     

On Suhl's approach to the Kondo problem

A model for the Kondo problem is studied in which the impurities are envisaged as a gas of infinitely heavy particles embedded in the gas of conduction electrons. Fors-wave interactions and low impurity concentrations the electron self-energy is expressed by the impurity-electron scattering matrix which is also shown to determine the thermodynamic potantial. Using standard Goldstone diagrams Suhl's equation is derived by the summation of leading singular graphs. For a special density of states, vanishing magnetic field, and no potential scattering the dispersion equation is solved exactly.     

A fractional approach to the Sturm-Liouville problem

The objective of this paper is to show an approach to the fractional version of the Sturm-Liouville problem, by using different fractional operators that return to the ordinary operator for integer order. For each fractional operator we study some of the basic properties of the Sturm-Liouville theory. We analyze a particular example that evidences the applicability of the fractional Sturm-Liouville theory.     

R-matrix approach to the 3-body problem

The asymptotic form of the Faddeev amplitude in coordinate space is derived in various orders. This form and the structure of the Faddeev equations allow by aR-matrix method to establish a set of equations directly for the 3-body on-shellT-matrix elements. The procedure is equally well suited for local and nonlocal interactions.     

Composite nucleon approach to the deuteron problem

A composite model is suggested for the nucleons by assuming a longrange strong gluon force between a diquark boson B and a quark A. In the proton, A is trapped inside B in an oscillator potential and, in the neutron, A is on the surface of B in a hydrogenlike state. Nucleon form factors are obtained in agreement with experiments. The model contains a mechanism for a large effective mass of the quark A. When B is identified with π and A with μ, one can fix the gluon charge value and obtain the magnetic moments of the proton and neutron. The (πμ) atomic model for the nucleon can be used to construct the deuteron on a hydrogen molecule model. It leads to values for the binding energy, electric quadrupole moment, and form factors of the deuteron that are in agreement with experiments.     

Density matrix approach to the Hartree-Fock problem

The problem of determining the best one-body density matrix which minimizes the total energy of a many fermion system is studied, with the idea of providing an alternative approach to the method of Roothaan for solving the Hartree-Fock equation.     

A new experimental approach to two-dimensional percolation

By using a computer to generate random patterns and then reproducing these patterns by photolithographic techniques, we have prepared a random stick system and a bond percolation system for experimental studies of 2D percolation. The agreement between the measured conductivity exponents for these two systems supports the universality hypothesis.